Related papers: On the Local Correctness of L^1 Minimization for D…
Sparse representation over redundant dictionaries constitutes a good model for many classes of signals (e.g., patches of natural images, segments of speech signals, etc.). However, despite its popularity, very little is known about the…
We consider the decomposition of a signal over an overcomplete set of vectors. Minimization of the $\ell^1$-norm of the coefficient vector can often retrieve the sparsest solution (so-called "$\ell^1/\ell^0$-equivalence"), a generally…
Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically formulate the dictionary learning problem as an optimisation with respect to two variables, i.e., dictionary…
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in…
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features in the presence of noise are lacking. Here, we provide very…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology…
We present a probabilistic modeling and inference framework for discriminative analysis dictionary learning under a weak supervision setting. Dictionary learning approaches have been widely used for tasks such as low-level signal denoising…
This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded.…
Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines,…
In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…
This paper provides fundamental limits on the sample complexity of estimating dictionaries for tensor data. The specific focus of this work is on $K$th-order tensor data and the case where the underlying dictionary can be expressed in terms…
Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient,…
In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new…
Dictionary learning consists of finding a sparse representation from noisy data and is a common way to encode data-driven prior knowledge on signals. Alternating minimization (AM) is standard for the underlying optimization, where gradient…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…